Question

The value of k for which both the roots of the equation

4x² – 20 kx + (25 k² + 15k – 66) = 0 are less than 2, lies in –

• A. (4/5, 2)
• B. (0, 2)
• C. (–1, –4/5)
• D. (–, –1)

Answer 1

Answer: (D)

(–, –1)

Answer 2

D ³ 0

Ž 400 k² – 4.4 (25 k² + 15 k – 66) ³ 0

Ž k £ 22/5

Now

A f(2) > 0 Ž 4(25 k² – 25 k – 50) > 0

Ž (k + 1) (k – 2) > 0

Ž kĪ (–, –1) 4 (2,)

$\frac{- b}{2a}$< 2 Ž $\frac{20k}{8}$< 2 Ž k < 4/5

\ k Ī (–, –1)